Students use number lines that extend in both directions and use 0 and 1 to locate integers and rational numbers on the number line. Students know that the sign of a nonzero rational number is positive or negative, depending on whether the number is greater than zero (positive) or less than zero (negative), and use an appropriate scale when graphing rational numbers on the number line.
Students know that the opposites of rational numbers are similar to the opposites of integers. Students know that two rational numbers have opposite signs if they are on different sides of zero, and that they have the same sign if they are on the same side of zero on the number line.
What is a rational number?
A rational number is a number that can be written as a fraction.
A decimal is rational if it terminates or repeats with a pattern.
1. Write the decimal equivalent of each fraction.
c. 6 7/10
2. Write the fraction equivalent of each decimal.
c. 36.90 Example 1: Graphing Rational Numbers
If b is a nonzero whole number, then the unit fraction 1/b is located on the number line by dividing the segment between 0 and 1 into b segments of equal length. One of the b segments has 0 as its left endpoint; the right endpoint of this segment corresponds to the unit fraction 1/b
Locate and graph the number 3/10 and its opposite on the number line.
Use what you know about the points - 7/4 and its opposite to graph both points on the number line below. The fraction, - 7/4, is located between which two consecutive integers? Explain your reasoning.
Example 2: Rational Numbers and the Real World
The water level of a lake rose 1.25 feet after it rained. Answer the questions below using the diagram below.
a. Write a rational number to represent the situation.
b. What two integers is 1.25 between on a number line?
c. Write the length of each segment on the number line as a decimal and a fraction.
d. What will be the water level after it rained? Graph the point on the number line.
e. After two weeks of rain, the water level of the lake is the opposite of the water level before it rained. What will be the new water level? Graph the point on the number line. Explain how you got your answer.
f. State a rational number that is not an integer whose value is less than 1.25 , and describe its location between two consecutive integers on the number line.
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